Hurdling the Bar

How do you hurdle the bar?
OBJECTIVE: To learn how to convert repeating decimals to fractions
[br]In a previous lesson, you learned how to convert [color=#0000ff]FRACTIONS[/color] to [color=#0000ff]DECIMALS [/color]by dividing the numerator by the denominator. [br][br][i][color=#0000ff]Getting to the Point:[/color] [/i]https://www.geogebra.org/m/wz32mw3y[br][br]In that lesson, you discovered that doing so sometimes leads to [color=#0000ff]TERMINATING DECIMALS[/color], but at other times, you get [color=#0000ff]REPEATING DECIMALS[/color]. In another lesson, you learned how to convert [color=#0000ff]TERMINATING DECIMALS[/color] to [color=#0000ff]FRACTIONS[/color].[br][i][br][color=#0000ff]Missing the Point:[/color][/i] https://www.geogebra.org/m/vjjpprfm[br][br]In this lesson, you're going to learn how to convert [color=#0000ff]REPEATING DECIMALS[/color] to [color=#0000ff]FRACTIONS[/color].[br][br]Here are the steps:[br][br]Step 1: Separate the integral part and the decimal part of the number.[br][br]Step 2: Convert the decimal part into a [color=#0000ff]PROPER FRACTION [/color]as follows:[br][br] (1) Write the numerator as the difference between number formed by the decimal digits and the number formed by the nonrepeating digits.[br][br] (2) Write the denominator as a series of 9's and 0's, representing each repeating digit as 9 and each nonrepeating digit as 0.[br][br] (3) Reduce the resulting fraction to lowest terms.[br][br]Step 3. Write the integral part and the fraction as a mixed number.[br][br]Examples:[br][br][img]data:image/png;base64,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[/img][br][br][img]data:image/png;base64,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[/img][br][br][img]data:image/png;base64,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[/img]
Below is a set of problems involving converting repeating decimals to fractions.
Converting Repeating Decimals to Fractions
ANSWER BOX:
[br]Check your answers below.
Converting Repeating Decimals to Fractions_Answer Key
In this lesson, you learned how to convert repeating decimals into fractions.
In future lessons, you'll learn more about decimals and fractions. Hope you had FUN today!
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